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TRANSCRIPT
Analysis of Distribution Systems with DSTATCOM
Thesis submitted in the partial fulfillment of the requirements for the award of
the degree of
Master of Engineering
in
Power Systems & Electric Drives
Thapar University, Patiala
By
Biswa Bhusan Sahoo
Roll No: 800841006
Under the supervision of
Dr. Sanjay K. Jain
Assistant Professor, EIED
JULY 2010
ELECTRICAL & INSTRUMENTATION ENGINEERING DEPARTMENT
THAPAR UNIVERSITY PATIALA-147004
iii
ABSTRACT
Distribution system, as the name suggest, is the medium through which power is
distributed among the end consumers. Among the distribution systems, Radial Distribution
System is popular due to cost and operational issues. In such systems due to high R/X ratio of the
cables/lines, the voltage decreases as moved away from the source and results in high losses.
Such issues of poor voltage regulation, high loses are related to the reactive power deficiency.
This problem of poor voltage or reactive power compensation can be minimized or sometimes
overcome by using suitable FACTS devices such as DSTATCOM. The DSTATCOM is also
capable of solving various power quality issues such as voltage unbalance etc. DSTATCOMs are
voltage source inverter (VSI) based devices, which regulate distribution bus voltage using
reactive power compensation.
The work reported in this thesis is carried out with the objective of identifying the
optimal location of DSTATCOM, as well as to carry out load flow analysis with a given rating of
DSTATCOM. For these purpose two stage methodologies is used. In the first stage pre-
compensated load flow of the distribution system is performed. On the basis of load flow
solution the voltage drop in each bus is observed. DSTATCOM is applied individually, one by
one to those buses which are below the safe limit. After compensation the Rate of Under Voltage
Mitigated Nodes (RUVMN) of that compensation are computed. This process is carried out for
each bus and the optimal location of DSTATCOM is computed upon these two parameters.
Load flow is realized using Backward β Forward sweep algorithm and the effectiveness
is tested on 33 and 69 Bus radial distribution system.
iv
TABLE OF CONTENTS Page No.
Certificate i
Acknowledgement ii
Abstract iii
Table of contents iv
List of figures vi
List of tables viii
CHAPTER-1 INTRODUCTION 1
1.1 Overview 1
1.2 Literature review 2
1.3 Objective of the work 5
1.4 Organization of the Thesis 5
CHAPTER-2 DISTRIBUTION SYSTEM LOAD FLOW AND DSTATCOM
PLACEMENT 6
2.1 Introduction 6
2.2 Load Flow of Radial Distribution System 7
2.2.1 Identification of the End Nodes and the Back Propagation Paths 7
2.2.2 Identifying Downstream Nodes of the Desired Node 8
2.2.3 Forward and Backward Sweep 8
2.2.4 Solution Methodology 8
2.3 Algorithm for Distribution System Load Flow 9
2.4 Mathematical model of DSTATCOM 12
2.5 Load flow using DSTATCOM 17
2.6 Rate Of Under Voltage Mitigated Nodes (RUVMN) 17
2.7 Algorithm for DSTATCOM Allocation 18
2.8 Conclusion 20
CHAPTER-4 RESULTS AND DISCUSSION 21
3.1 DSTATCOM Placement on 33-Bus RDS 21
3.2 DSTATCOM Placement on 69-Bus RDS 32
3.3 Conclusion 43
v
CHAPTER-5 CONCLUSIONS AND SCOPE FOR FUTURE WORK 44
4.1 Conclusions 44
4.2 Scope for future work 44
References 45
Appendix A 47
Appendix B 49
vi
LIST OF FIGURES
Figure No. Figure Name Page No.
Figure 2.1: Flow chart for load flow solution of radial
distribution system 11
Figure 2.2: A typical model of DSTATCOM for compensation of
reactive power
12
Figure 2.3: Single line diagram of two buses of a distribution
system
12
Figure 2.4: Phasor diagram of voltages and current of the
system shown in Fig 2.2 13
Figure 2.5: Single line diagram of two buses of a distribution
system with D-STATCOM consideration
13
Figure 2.6: Phasor diagram of voltages and currents of the
system shown in Fig.2.4
14
Figure 2.7: Flow chart of radial distribution system with
DSTATACOM 19
Figure 3.1: 33-Bus Radial Distribution System 22
Figure 3.2: Graph between Bus Voltage and Number of Buses
for 33-Bus RDS
25
Figure 3.3: A Comparison between voltage profile of Bus 3, 6, 28,
32 after DSTATCOM placement on these nodes
27
Figure 3.4: Graph comparing the Rate of under voltage
mitigation for all 33- Buses 29
Figure 3.5: Comparison of compensation at buses 3,6,28,32 of
33-Bus Radial Distribution System 32
Figure 3.6: 69-Bus Radial distribution System 33
vii
Figure 3.7: Plot for Load Flow Results of 69-Bus Radial
Distribution System
37
Figure 3.8: Plot Comparing Improvement in Voltage Profile of
Buses 8,59,57
39
Figure 3.9: RUVMN for 69-Bus Radial Distribution System
41
viii
LIST OF TABLES
Table No. Table name Page No.
Table 3.1 Tabulation of all downstream nodes for a given node 23
Table 3.2 Voltage magnitude and Phase angle from 33-bus
Radial Distribution system Load flow solution 24
Table 3.3 Voltage magnitude Comparison for some test buses
after DSTATCOM attachment 26
Table 3.4 Tabulation for RUVMN of 33-Bus Radial
Distribution System
28
Table 3.5 Comparison of Compensation Between Buses 3,6,28
and 32 for Variable rating DSTATCOM. 30
Table 3.6 Comparison of Compensation Between Bus No. 3 , 6,
28 and 32 with a fixed 2 MVAr rating DSTATCOM
31
Table 3.7 RUVMN For a given 2 MVAr DSTATCOM In 33
Bus Distribution System
34
Table 3.8 Downstream nodes for each node in 69-Bus Radial
Distribution System 36
Table 3.9 Comparison of Compensation between Bus No. 8,59
and 57 with Variable DSTATCOM
38
Table 3.10 RUVMN of variable DSTATCOM Rating for a 69-
Bus Radial Distribution System
40
Table 3.11 ComparisonbetweenBusvoltageofBusNo.8,27,69using
Variable rating DSTATCOM
42
1
CHAPTER 1
INTRODUCTION
1.1 OVERVIEW
An electric distribution system is part of an electric system between the bulk
power source or sources and the consumers service switches. The bulk power sources are
located in or near the load area to be served by the distribution system and may be either
generating stations or power substations supplied over transmission lines. Distribution
systems can, in general, be divided into six parts, namely, sub transmission circuits,
distribution substations, distribution or primary feeders, distribution transformers,
secondary circuits or secondaryβs, and consumerβs service connections and meters or
consumerβs services.
With an increase in load demand, burden on lines and the voltage level is
challenged. Now a dayβs maintaining voltage magnitude at an acceptable range is one of
the major system constraints. One of the classical methods to solve this is to place shunt
capacitor in line. But the reactive power provided by the shunt capacitor is bus voltage.
This may reduce its effectiveness in high and low voltages. Another problem related to
shunt capacitor is that they resonate when got tuned with system reactance.
Although the concept of FACTS was developed originally for transmission
network; this has been extended since last 10 years for improvement of Power Quality
(PQ) in distribution systems operating at low or medium voltages. Apart from all other
technical advances, these FACTS devices respond quickly to the changes in network
condition unlike to shunt capacitor. Distribution STATCOM (D-STATCOM) is a shunt
connected voltage source converter which has been utilized to compensate bus voltages
2
or reactive VARs. However to achieve this goal, size and placement of the device is an
important consideration.
1.2 LITERATURE REVIEW
The issues like low voltage, voltage dip, voltage sag etc. have been the major
challenge faced by power engineer since two to three decades. Even though transfer of
electricity is getting complex and sophisticated day by day, there is no end for the hunt of
a regulated voltage profile i.e., better quality. In earlier stages improvement was done by
conventional devices such as synchronous condensers, tap-changing transformer,
capacitor placement etc. But with improvement of Power Electronic equipments a new
dimension has been achieved. Among these devices, DSTATCOM has turned out to be
promising tool for such quality improvements. To place the DSTATCOM in distribution
system, the load flow analysis of the network is needed to be performed.
Load flow analysis of distribution system differs from transmission system to the
fact that, tough distribution systems are generally radial, unbalanced operation and
loading conditions, non-linear load models, dispersed generation and have a high R/X
ratio, the conventional Newton- Raphson (NR) and fast decoupled load-flow methods
find it difficult to generate a conversed result. Numerous efforts have been made to
develop power flow algorithms for distribution systems. One of the most typical among
these methods is the Forward and backward sweep methods or ladder networks theory [1-
5]. These methods take advantage of a natural feature of the radial networks, i.e., there is
a unique path from any given bus to the source. The general algorithm consists of two
basic steps: forward sweep and backward sweep.
Salama [3] have presented a very simple but robust method β the ladder formula.
Essentially, the ladder network method treats the radial system as two basic element
types: the network natural elements (impedance) and voltage control current sources
(system loads) at each load node. The forward sweep is mainly a voltage drop calculation
from the sending end to the far end of a feeder or a lateral; and the backward sweep is
3
primarily a current summation based on the voltage updates from the far end of the feeder
to the sending end. Then by using KVL and KCL, the voltage drop can be obtained.
Berg [4] presented a backward method in 1967, which used a backward
procedure to update the equivalent impedance at the sending end. The main idea of this
method is to treat the load as constant impedance. So if the equivalent impedance is
convergent, the whole system convergence will be reached.
Baran [5] presented a forward method in 1989. In this method, the sending end
voltage becomes the main concern of the system convergence. Voltage drop and the
information on system structure have been considered in the forward sweep. The voltage-
sensitive load current can be included in the system model.
There has been a lot of literature on placement of capacitor in distribution system
for power quality improvement. Perez [6], proposed a very simple algorithm for optimal
capacitor placement. His algorithm is based on the fact that the branch current
incremental due to a capacitor placed at a bus, under two different cases where another
capacitor is placed at two different buses, is approximately equal. He has taken into
consideration loss sensitive factor and size of capacitor for the placement of capacitor.
Apart from normal algorithms many paper deals with advanced search techniques
for capacitor placement. Balakumaran [7] has used fuzzy technique for capacitor
placement, to have maximum loss reduction in the system. A sequence of nodes for
capacitor placement has been identified by repetitive application of loss minimization
technique using a single capacitor. After getting the nodes values, size of the capacitor to
be placed at that node is determined by minimizing the loss saving equation with respect
to capacitor current.
Kyu-Ho Kim [8] has considered unbalanced distribution network for capacitor
placement to improve voltage profile using GA (genetic Algorithm). A gradual load
variation is also taken into account. Hiroyuki Mori[9] have used parallel tabu search for
distribution system capacitor placement. A comparison between different techniques such
as Simulated Annealing (SA), Genetic Algorithm (CA), and Tabu Search (TS) has been
4
stressed and an effective algorithm is generated for capacitor placement in tabu search
platform.
Due to the advancements in the area of power electronic advances over
conventional method of power quality control many has concentrated on the application
of these devices known as FACTS devices for power system. In 1995, the first
STATCOM was installed at the Sullivan substation of Tennessee Valley Authority
(TVA) in northeastern Tennessee. This unit is mainly used to regulate bus voltage during
the daily load cycle to reduce the operation of the tap changer. Since then much work has
been done on modeling, simulation and installation of a STATCOM in electrical network
[10-12]. Now a dayβs STATCOM is readily installed in Distribution System with a
reduced rating and is named as Distribution STAtic COMpensator (DSTATCOM).
Haque [13] considered the effect of DSTATCOM in voltage profile improvement
both with and without active power injection. He compares the performance of DVR
(Dynamic voltage regulator) with DSTATCOM. His observation were that, amount of
apparent power injection required by a D-STATCOM to correct a given voltage sag is
much higher than that of a DVR. The advantage of using DSTATCOM to that of a DVR
is that, it can correct the voltage sag on both side where as a DVR can correct it only in
downstream . It was also observed that DSTATCOM can correct much higher voltage sag
without injecting any active power into the system as compared to DVR.
Sensarma[14] considered the problem of voltage compensation at PCC, at the
end of a distribution line using a 8 KVA STATCOM. He derived the small-signal model
of the system with a distribution line and also considered the compensation of sub-cycle
voltage transients.
These works were concentrated for small network and for short duration of time.
Ramsay [15] considered the application of D-STATCOM for distribution voltage
regulation on long, voltage-limited feeders. He successfully compared the superiority of
DSTATCOM over conventional methods like capacitor placement and voltage regulators.
In his study, two types of distribution lines have been considered, each serving different
types of loads; uniformly distributed and lumped. Low density distribution feeders which
5
are typically found in rural systems has been characterized into one of these line.
Husseini et al. [16] has presented the modeling of DSTATCOM suited for radial
distribution system load flow.
1.3 OBJECTIVE OF THE WORK
Objective of the present work is to study and implement the DSTATCOM model
in the load flow and identify the nodes for DSTATCOM placement. The compensation
resulted by operating the DSTATCOM in fixed rating mode and complete compensation
mode is also to be investigated.
1.4 ORGANISATION OF THE THESIS
The work carried out in this Thesis has been summarized in five Chapters. The
Chapter 1 highlights the brief introduction, summary of work carried out by various
researchers, and the outline of the Thesis. The Chapter 2 explains load flow technique
using backward and forward sweep, DSTATCOM model suited for load flow and
DSTATCOM allocation strategy. Chapter 3 deals with results and discussion pertaining
to two test cases, namely 33 bus RDS and 69 bus RDS. The conclusions and the scope of
further work are detailed in Chapter 4.
6
CHAPTER 2
DISTRIBUTION SYSTEM LOAD FLOW AND
DSTATCOM PLACEMENT
2.1 INTRODUCTION
The load flow as the name suggest is study of flow of power in a network to meet
the load demand at different nods. With the rise in population, demand of load is having a
steep rise to that of time. So study of load flow may solve lot of issues such as planning
and forecasting, design, operation and control of electrical power. A detail study of the
characteristics of load flow will give us bus voltage, branch current, real power flow,
reactive power flow for a specific generation and load condition.
To perform load flow analysis, various classical methods have been proposed
such as Gauss-Seidel, Newton-Raphson etc. These methods are found to be suitable more
for a transmission system rather than a distribution system. The major reason behind it is
that, both have a different topology and R/X ratio of the distribution system is much
higher than that of the transmission system which makes conventional methods difficult
to converse.
Some other inherent characteristics of electric distribution systems are (i) Radial
or weakly meshed structure (ii) unbalanced operation and unbalanced distributed loads
(iii) large number of buses and branches (iv) It has wide range of resistance and reactance
values (v)Distribution system has multiphase operation.
The load flow technique forms the foundation for implementation of any
improvising tool in a distribution system. Tough load flow solution runs iteratively, itβs a
time consuming process. Hence fastness is the major concern. A very simple and
fundamental method of load flow analysis which is based on two basic laws in electrical
engineering, the Kirchhoffβs current and voltage law is used. Since specially formulated
7
for the power flow of a distribution system, which is usually, radial in configuration, it is
fast and very effective tool for simulation where speed is a factor.
2.2 LOAD FLOW OF RADIAL DISTRIBUTION SYSTEM
In the forgoing Load flow methodology, the major features to be considered are as
follows:
Formation of the node and branch matrix M
Identification of the end nodes and back propagation paths
Identifying downstream nodes of the desired node
Forward and Backward sweep
Solution Methodology
The very first step to perform in load flow is to generate a matrix M (with n columns
as nodes and n-1 rows equal to number of branches). It is understood that each branch has
a sending end node and a receiving end node. So this matrix is so formulated that, for a
particular branch (row), the sending end node of a branch is assigned -1 and that of
receiving end as +1. Rest elements in that row are assigned 0.
2.2.1 IDENTIFICATION OF THE END NODES AND THE BACK
PROPAGATION PATHS
Form the obtained M matrix, it is observed that, the column which represent the
end nodes donβt have -1, because the end nodes can only be the receiving node of a
branch. After identification of end node (identifying position of 1 in that column ),
corresponding row gives the branch attached to it and in this row, -1 value is identified.
The corresponding column gives the sending end node to the studied branch. This
searching process continues until the algorithm reaches a column which has no element
equal to 1. This column represents the source node.
8
2.2.2 IDENTIFYING DOWNSTREAM NODES OF THE DESIRED NODE
After obtaining the end nodes and back propagation paths (nodes connected in
between the end node and the source node), all the downstream nodes for a desired node
are found out easily.
2.2.3 FORWARD AND BACKWARD SWEEP
Forward/backward sweep-based power flow algorithms generally take advantage
of the Radial network topology and consist of forward and/or backward sweep processes.
In these types of algorithms, developed, the forward sweep is mainly the node Voltage
calculation from the sending end to the far end of the feeder and laterals, and the
backward sweep is primarily the branch current and/or power summation from the Far
end to the sending end of the feeder and laterals.
Most of the distribution system power flow algorithms employ KVL and
Kirchhoffβs Current Law (KCL) to calculate the node voltages in the forward and
backward processes. The radial part is solved by a straightforward two-step procedure in
which the branch currents are first computed (backward sweep) and then the bus voltages
are updated (forward sweep) by using Eqn. 2.1 for each branch.
2.2.4 SOLUTION METHODOLOGY
After obtaining the downstream nodes of all nodes and with an assumption that
three-phase radial distribution system is balanced, load flow solution is initiated. Voltage
of node i can be expressed as:
π π = π π β 1 β πΌ π π(π) 2.1
where V(i) and V(iβ1) are the voltage of nodes i and iβ1 respectively, Z(i) is the
impedance of line i, I(i) is the current flow in line i. Since the voltage of source node is
known (1 pu.), Eqn.2.can be used in the forward sweeps to determine the voltage of other
nodes in the distribution systems. The load current of node i, πΌπΏ(i), can be written as:
πΌπΏ (π) =ππΏ π β ππΏ(π)
πβ(π) 2.2
9
where ππΏ(i) and ππΏ(i) are active and reactive power of load connected to node i,
respectively. The current through a branch i, i.e. I(i), equals πΌπΏ(i) plus the sum of the
branch currents connected to this line:
πΌ(π) = πΌπΏ(π) + πΌπ βπ½π(j) 2.3
where π½π is the set consisting of all branches downstream to node i. Thus, π½π is empty for
each end node. As a result, I(i) connected to the end nod i can be expressed as:
πΌ π = πΌπΏ(π) 2.4
2.3 ALGORITHM FOR DISTRIBUTION SYSTEM LOAD FLOW
The flow chart of the algorithm is shown in Fig. 2.1. The algorithm steps for load
flow solutions of distribution system are given as :
Step1: Read the distribution system line data and load data.
Step 2: Form the node and branch matrix M by steps given in 2.2.1.
Step 3: Get end nodes and the back propagation paths by following steps given in
2.2.2.
Step 4: Obtain the value of π½π of Eqn. 2.3 by calculating the downstream nodes of
every node.
Step 5: Make a flat start by assuming the voltage profile of all bus to be 1 pu.
Step 6: Iteration k = k + 1.
Step 7: Calculate the load current πΌπΏ(π) of each bus using Eqn. 2.2
10
Step 8: Summation of all the load currents corresponding to the nodes which are
downstream to the desired node, as well as its own node; gives the current
injected I(i) at that node.
Step 9: After calculating the current injected to each bus, calculate the voltage of
each bus using Eqn.2.1
Step 10: compare the difference between each consecutive voltage values of every
node. This will give DV (deviation).
Step 11: If DV is not less than equal to the given tolerance limit then, update the
new voltage values and Go to Step 7. Else display the Absolute vale of
Voltage and the phase angle.
Step 12: STOP
11
START
READ NECESSARY LINE AND BUS DATA
FORM A ROW, COLUM MATRIX M
OBTAIN THE END NODES AND BACK
PROPAGATION PATHS FROM MATRIX M
OBTAIN ALL THE DOWNSTREAM BUSES FOR
EACH BUS
MAKE A FLAT START WITH ALL BUS VOLTAGES AS
1p.u
SET ITERATION COUNT K=1
CALCULATE THE LOAD CURRENTASWELL AS LINE
CURRENT USING Eqn.2.2 AND Eqn.2.3
RESPECTIVELY
CALCULATE THE BUS VOLTAGES USING Eqn 2.1
FIND THE DEVIATION DV BETWEEN CONSUCUTIVE
ITERATIONS
IF DV<EPS. ,FOR ALL NODE n
YES
DISPLAY THE ABSOLUTE VALUE OF VOLTAGE AND
PHASE ANGLE OF EACH NODE
STOP
INCREMENT K=K+1 AND
UPDATE THE VOLTAGE
VALUES
NO
Fig. 2.1 Flow chart for load flow solution of radial distribution system
12
2.4 MATHEMATICAL MODELING OF DSTATCOM
DSTATCOM is a shunt device which hast the capability to inject or absorb both
active and reactive current. The reactive power output of a D-STATCOM is proportional
to the system voltage rather than the square of the system voltage, as in a capacitor. This
makes DSTATCOM more suitable rather than using capacitors. Though storing energy is
a problem for long term basis, considering real power compensation for voltage control is
not an ideal case. So most of the operations considered is steady stat only and the power
exchange in such a condition is reactive. To realize such a model, it can be said that a
DSTATCOM consists of a small DC capacitor and a voltage source converter
Voltage source
Converter
+_
VS
IDSTATCOM
VDC
Fig. 2.2 A typical model of DSTATCOM for compensation of reactive power
To model a DSTATCOM in distribution system, a simple single line diagram of two bus
distribution line is shown in figure 3.3.
Vi VjR X
IL
PLi+jQLi PLj+jQLj
Fig . 2.3 Single line diagram of two buses of a distribution system.
13
To analyze it, it is assumed that one of the bus is a reference bus and the other has a
lower voltage profile than that of the reference bus. Here ππ is the reference bus and ππ is
the desired bus for compensation. Now it is desired to compensate the bus voltage of ππ to
1 p.u. by using DSTATCOM. The phasor diagram of the shown single line diagram is
expressed as:
Vi
LRILjX
jV
Fig.2.4 Phasor diagram of voltages and current of the system shown in Fig 2.2
From this phasor diagram it is drawn that
ππβ πΌ = ππβ πΏ β ππΌπΏβ π 2.5
where ππβ πΌ and ππβ πΏ are the voltage of buses j and i before compensation respectively,
Z=R+ j X is the impedance between buses i and j, πΌπΏ β π is the current flow in line.
Voltage ππβ πΏ and current πΌπΏ β π are the values which are derived from the load flow
calculations. Figure shown below gives a better idea of operation of DSTATCOM in
steady state analysis.
VβiR X
IβL
Voltage source
Converter
+_
PLj+jQLj
IDSTATCOM
Fig.2.5 Single line diagram of two buses of a distribution system with
D-STATCOM consideration.
14
Here DSATACOM is used to regulate the voltage of bus j. As it is mentioned that only
reactive power compensation is considered, so the current drawn by the DSTATCOM
(Iπ·βπππ΄ππΆππ ) is in quadrature with the system voltage. To visualize the impact of
DSTATCOM over the system phasor diagram of the complete system is drawn.
' i'V
LRI'
LjX 'jV '
'
LI'
DSTATCOMI
DSTATCOMnew RIDSTATCOMjXI
jnewV
Fig.2.6 Phasor diagram of voltages and currents of the system shown in
Fig.2.4
Mathematical analysis of the phasor diagram shown in Fig. 2.6 implies that
β πΌπ·πππ΄ππΆππ =π
2+ πΌπππ€ ,πΌπππ€ < 0 2.6
πππππ€ β πΌπππ€ = ππβ²β πΏ β² β π + ππ πΌπΏ
β²β πβ² β
π + ππ πΌπ·πππ΄ππΆππ β πΌπππ€ +π
2 . 2.7
Where Iπ·βπππ΄ππΆππβ (πΌπππ€ +π
2) is the injected current by DSTATCOM , Vπ πππ€
β πΌπππ€ is the voltage of bus j after compensation by DSTATCOM. πβ²πβ πΏβ² is the voltage
of bus i after compensation. πΌβ²πΏ β πβ² is derived from load flow calculations. Separating
the real and imaginary parts of Eqn.2.7 yields:
15
Vπ πππ€ cosπΌπππ€ = Re (πβ²πβ πΏ) + πIπ·βπππ΄ππΆππ sin(πΌπππ€ +π
2)
βπ π( ππΌβ² πΏ β πβ² ) β π Iπ·βπππ΄ππΆππ cos(πΌπππ€ +π
2). 2.8
Vπ πππ€ sin πΌπππ€ = πΌπ(π β²πβ πΏβ² ) βπIπ·βπππ΄ππΆππ cos(πΌπππ€ +
π
2)
β πΌπ ππΌβ² πΏ β πβ² β π Iπ·βπππ΄ππΆππ sin(πΌπππ€ +π
2). 2.9
Furthermore these two equations can be modified using the following notations:
π1 = π π π β²πβ πΏ
β² β Re ππΌβ² πΏ β πβ² .
π2 = πΌπ π β²πβ πΏ
β² β Im ππΌβ² πΏ β πβ² .
π = Vπ πππ€
c1 = βπ
c2 = βπ
π₯1 = Iπ·βπππ΄ππΆππ
π₯2 = πΌπππ€
Eqn. 2.10 and 2.11 are obtained from Eqn. 2.8 and 2.9 as follows:
π cos π₯2 = π1 β c1π₯1 sin π₯2 β c2π₯1 cos π₯2 2.10
π sin π₯2 = π2 β c2π₯1 sin π₯2 + c1π₯1 cosπ₯2 2.11
where π1, π2, π1πππ π2are constants, π is the magnitude of compensated voltage (1 p.u.)
and π₯1,π₯2 are variables to be determined. From the above two equations it can be shown
that
π₯1 = π cos π₯2βπ1
β c1 sin π₯2β c2 cos π₯2 2.12
and
π₯1 = π sin π₯2βπ2
β c2 sin π₯2+ c1 cos π₯2 2.13
16
Now by equating Eqn.2.12 and Eqn.2.13 and eliminating π₯1 , we get
π1 π2 β π2π1 sin π₯2 + βπ1 π1 β π2π2 cos π₯2 + ππ1 = 0 3.14
Consideringπ₯ = sin π₯2, following equations is derived
π12 + π2
2 π₯2 + 2π1ππ1 π₯ + π2π12 β π2
2 = 0 2.15
where,
π1 = π1 π2 β π2π1,
π2 = π1 π1 + π2π2,
Therefore,
π₯ =βπ΅Β± β
2π΄.
Where
β= π΅2 β 4π΄πΆ
π΄ = π12 + π2
2,
π΅ = 2π1ππ1,
πΆ = π2π12 β π2
2,
From the roots of x, πΌπππ€ value is obtained as π₯2 = πππ sin π₯ and π₯2 =,πΌπππ€ . From
these values π₯1 = Iπ·βπππ΄ππΆππ is found out. Hence injected reactive power by
DSTATCOM is given by
πππ·βπππ΄ππΆππ = ππ πππ€ πΌπ·βπππ΄ππΆππβ 2.16
Where
π½π πππ€ = ππ πππ€ β πΌπππ€ 2.17
ππ·βπππ΄ππΆππ = Iπ·βπππ΄ππΆππβ (πΌπππ€ +π
2) 2.18
Now this reactive power is compensated from the reactive power drawn at the desired
bus. This compensation improves the voltage profile of the desired bus to 1 p.u and
improves the voltage profile of neighboring buses (mostly the downstream buses).
17
2.5 LOAD FLOW USING DSTATCOM
To incorporate DSTATCOM in distribution system, first load flow analysis is
done without compensation. Now the constraint which is implemented is that, voltage
profile below 0.95 p.u or above 1.05 p.u is considered as under voltage or over voltage
buses respectively. These buses are needed to be compensated. From the load flow
results, buses with under voltage or over voltage profile are selected. DSTATCOM is
attached on one of those buses and again load flow analysis is performed. Like this all the
under voltage and over voltage buses are compensated individually and results were
obtained.
There are two modes of incorporating a DSTATCOM in load flow analysis. One
with complete compensation (compensating the desired bus voltage to 1 p.u) and
compensation with a set rating of DSTATCOM.
It is first assumed that the voltage magnitude in the node where DSTATCOM is
located be 1 p.u. then the phase angle of the voltage and the reactive power injection is
calculated from Eqn. 2.17 and Eqn. 2.16 respectively. Then, the new magnitude and
phase angle of the compensated node are utilized to determine the voltage of
DSTATCOM located downstream nodes in the forward sweep of load flow. If the
reactive power calculated from Eqn. 2.16 is greater than the maximum reactive power
rating of DSTATACOM, the injected reactive power of DSTATCOM is set to its
maximum rating and is considered as a negative constant value in load model in node j,
and the load flow program is solved in a normal way as if there is no D-STATCOM.
2.6 Rate Of Under Voltage Mitigated Nodes(RUVMN)
Once the load flow is performed using DSTATCOM in a particular bus, the
number of buses whose under or over voltage problems got mitigated is found out. The
percentage of improvement gives RUVMN (Rate of Under Voltage Mitigated Nodes).
The suggested locations for DSTATCOM are ordered in terms of RUVMN as well as the
required reactive power for compensation. Buses with highest percentage of RUVMN are
found to be suitable for DSTATCOM allocation
18
2.7 ALGORITHM FOR DSTATCOM ALLOCATION
Step 1: Read the distribution system branch impedance values and the bus real and
reactive power data.
Step 2: Run the Load Flow of Distribution System by using steps given in section 2.3,
to find out voltage magnitudes at the buses.
Step 3: Select the candidate bus by method given in section 2.6
Step 4: Assume the voltage profile of the candidate bus to be 1 p.u.
Step 5: Obtain the reactive power of the DSTATCOM and phase angle of the
compensated bus using section 2.4
Step 6: Update the reactive power and voltage phase angle at candidate bus.
Step 7: Run the Load Flow of Distribution System with updated reactive power at the
candidate bus.
Step 8: Calculate the RUVMN and RPR using section 2.6, for that bus.
Step 9: Similarly attach DSTATCOM in all the buses one by one and perform Step1 to
Step 8 in each case.
Step 10: End
19
START
READ NECESSARY LINE AND BUS DATA
PERFORM THE LOAD FLOW AS IN SECTION 2.3
SELECT THE BUS IN WHICH DSTATCOM IS TO BE
ATTACHED
ASSUME VOLTAGE PROFILE OF CANDIDATE BUS
AS 1 p.u
SET ITERATION COUNT K=1
CALCULATE THE LODE CURRENTASWELL AS LINE
CURRENT USING Eqn.2.2 AND Eqn.2.3
RESPECTIVELY
CALCULATE THE BUS VOLTAGES USING Eqn 2.1
FIND THE DEVIATION DV BETWEEN CONSECUTIVE
ITERATIONS
IF DV<EPS. ,FOR ALL NODE n
YES
DISPLAY THE ABSOLUTE VALUE OF VOLTAGE AND
PHASE ANGLE OF EACH NODE
STOP
INCREMENT K=K+1 AND
UPDATE THE VOLTAGE
VALUES
FIND REACTIVE POWER AND PHASE ANGLE BY TAKING DATA
FROM PREVIOUS LOAD FLOW SOLUTION AND MODELLING IT AS
IN SECTION 2.4 TO MAINTAIN CANDIDATE BUS VOLTGE 1 p.u
UPDATE THE BUS VOLTAGE AND SUBSTRACT THE REACTIVE
POWER OBTAINED, FROM THE REACTIVE POWER DRAWN BY
THE CANDIDATE BUS
NO
Figure 2.7 Flow chart of radial distribution system with DSTATACOM
20
2.8 CONCLUSION
In this chapter, forward and backward sweep method for load flow analysis is performed.
A mathematical model of DSTATCOM is proposed and is used to improve the
performance of the distribution network. RUVMN is taken as the selection criteria for
placement of DSTATCOM in the network. With these theories, a much needed
background for case study of DSATACOM placement in distribution system is achieved.
21
CHAPTER 3
RESULTS AND DISCUSSION
This chapter contains the results of the implementation of the theoretical content
discussed in Chapter 2, for two cases. These Algorithms are developed in MATLAB
environment and has been tested on 33 and 69 bus radial distribution system. Bus data
and line data of the 33 and 69 bus radial system is given in Appendix-A and Appendix-B
respectively.
RUVMN (Rate of Under Voltage Mitigation) has been taken as the criteria for
selection of the locations of DSTATCOM in the test module. Results have been divided
into two major parts.
CASE I : With fixed voltage (variable rating) DSATACOM
CASE II : With fixed rating DSTATCOM.
3.1 DSTATCOM placement on 33-Bus Radial Distribution
System
Following are the characteristics of the 33-bus radial distribution system shown in
Fig 3.1
Number of buses = 33
Number of lines = 32
Slack Bus No =1
Base Voltage=12.66 KV
Base MVA=100 MVA
22
3 4 5 6 7 8 9 10 11 18171615141312
32
30
27
S/S
19
1
25
24
23
22
21
20
26
28
29
31
2
33
Figure 3.1 33-Bus Radial Distribution System
For the above given network, we have to know the downstream nodes for each node, to
perform backward sweep calculations as per the Algorithm. Table 3.1 below shows the
downstream nodes behind every node.
23
Table 3.1 Tabulation of all downstream nodes for a given node.
Branch No. Sending End Bus. Receiving End Bus. Down Stream Node
1
1
2
2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 17 18 19 20 21 22 23 24 25 26 27 28
29 30 31 32 33
2
2
3
3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 23 24 25 26 27 28 29 30 31 32 33
3
3
4
4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 26 27 28 29 30 31 32 33
4
4
5
5 6 7 8 9 10 11 12 13 14 15 16 17 18
26 27 28 29 30 31 32 33
5
5
6
6 7 8 9 10 11 12 13 14 15 16 17 18
26 27 28 29 30 31 32 33
6 6 7 7 8 9 10 11 12 13 14 15 16 17 18
7 7 8 8 9 10 11 12 13 14 15 16 17 18
8 8 9 9 10 11 12 13 14 15 16 17 18
9 9 10 10 11 12 13 14 15 16 17 18
10 10 11 11 12 13 14 15 16 17 18
11 11 12 12 13 14 15 16 17 18
12 12 13 13 14 15 16 17 18
13 13 14 14 15 16 17 18
14 14 15 15 16 17 18
15 15 16 16 17 18
16 16 17 17 18
17 17 18 18
18 2 19 19 20 21 22
19 19 20 20 21 22
20 20 21 21 22
21 21 22 22
22 3 23 23 24 25
23 23 24 24 25
24 24 25 25
25 6 26 26 27 28 29 30 31 32 33
26 26 27 27 28 29 30 31 32 33
27 27 28 28 29 30 31 32 33
28 28 29 29 30 31 32 33
29 29 30 30 31 32 33
30 30 31 31 32 33
31 31 32 32 33
32 32 33 33
24
The load flow of the distribution system is obtained using the Algorithm discussed in
Chapter 2. The load flow result of 33-bus RDS without DSTATCOM compensation are
summarizes in Table 3.2
Table 3.2. Voltage magnitude and Phase angle from 33-bus Radial Distribution
system Load flow solution
Bus Number Voltage Magnitude in p.u. Angles in degree
1 1.0000 0
2 0.9970 0.0002
3 0.9829 0.0017
4 0.9754 0.0028
5 0.9679 0.0040
6 0.9495 0.0024
7 0.9459 -0.0017
8 0.9323 -0.0044
9 0.9260 -0.0057
10 0.9201 -0.0068
11 0.9192 -0.0067
12 0.9177 -0.0065
13 0.9115 -0.0081
14 0.9092 -0.0095
15 0.9078 -0.0102
16 0.9064 -0.0106
17 0.9044 -0.0119
18 0.9038 -0.0121
19 0.9965 0.0000
20 0.9929 -0.0011
21 0.9922 -0.0015
22 0.9916 -0.0018
23 0.9793 0.0011
24 0.9726 -0.0004
25 0.9693 -0.0012
26 0.9475 0.0030
27 0.9450 0.0040
28 0.9335 0.0055
29 0.9253 0.0068
30 0.9218 0.0087
31 0.9176 0.0072
32 0.9167 0.0068
33 0.9164 0.0067
25
OBSERVATION:
1. Total Number of Buses out of constraint limit: 21
2. Bus number out of constraint limit: 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ,
16,17, 18 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33
3. Total percentage of Buses out of constraint limit: 63.6364%
Figure 3.2 Graph between Bus Voltage and Number of Buses for 33-Bus RDS
CASE I : With fixed voltage DSATACOM
Once the load flow data is obtained, modeling of DSTATCOM is done using these data
and tested on the given 33-bus radial distribution system. A clear picture of the
performance of DSTATCOM is obtained by randomly selecting bus and attaching
DSTATCOM to it. Following are the results obtained after placing DSTATCOM on
some of the nodes.
0 5 10 15 20 25 30 350.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Bus Number
Bus V
oltage(in p
.u)
26
Table 3.3 Voltage magnitude Comparison for some test buses after
DSTATCOM attachment
Compensated buses β Compensated
bus no. 3
Compensated
bus no. 6
Compensated
bus no. 28
Compensated
bus no. 32 Bus No.β
1 1.0000 1.0000 1.0000 1.0000
2 0.9971 0.9971 0.9971 0.9970
3 1.0000 0.9835 0.9832 0.9830
4 0.9926 0.9763 0.9759 0.9756
5 0.9854 0.9693 0.9688 0.9682
6 0.9672 1.0000 0.9509 0.9499
7 0.9638 0.9967 0.9474 0.9464
8 0.9504 0.9837 0.9337 0.9328
9 0.9442 0.9778 0.9274 0.9264
10 0.9384 0.9722 0.9216 0.9206
11 0.9376 0.9714 0.9207 0.9197
12 0.9361 0.9700 0.9192 0.9182
13 0.9301 0.9641 0.9130 0.9120
14 0.9278 0.9620 0.9107 0.9097
15 0.9264 0.9606 0.9093 0.9083
16 0.9251 0.9593 0.9079 0.9069
17 0.9231 0.9574 0.9059 0.9049
18 0.9225 0.9568 0.9053 0.9043
19 0.9965 0.9966 0.9965 0.9965
20 0.9930 0.9930 0.9930 0.9929
21 0.9923 0.9923 0.9923 0.9922
22 0.9916 0.9917 0.9916 0.9916
23 0.9965 0.9799 0.9797 0.9794
24 0.9899 0.9732 0.9730 0.9727
25 0.9867 0.9699 0.9697 0.9694
26 0.9653 0.9982 0.9491 0.9480
27 0.9628 0.9957 0.9467 0.9455
28 0.9516 0.9849 1.0000 0.9343
29 0.9436 0.9771 0.9923 0.9263
30 0.9401 0.9738 0.9890 0.9229
31 0.9360 0.9698 0.9852 0.9189
32 0.9351 0.9690 0.9843 1.0000
33 0.9348 0.9687 0.9840 0.9997
27
From Table 3.3 we can see that placement of DSTATCOM improves the voltage profile
of the desired bus to 1 p.u and it also improves the voltage profile of neighboring buses.
After placing DSTATCOM on bus no. 6, it is seen that V p.u of bus no.6 is 1 p.u as well
as there is 63.63% under voltage mitigation.. Similarly improvement of voltage profile,
after compensation on Bus no. 3,28 and 32 can be seen.
Figure 3.3 A Comparison between voltage profile of Bus 3, 6, 28, 32 after
DSTATCOM placement on these nodes.
As per Chapter 2, RUVMN forms the criteria for selection of suitable buses for
DSTATCOM Placement. Now our aim is to find out the buses in which, after placing
DSTATCOM, there is maximum improvement of voltage profile in the neighboring
buses as well as its own voltage profile gets improved. In other words, DSTATCOM is
placed on all the buses, and the nodes which are violating the constraint limits after
DSTATCOM placement are found out. Hence a observation is made by comparing the
constraint violating buses before and after the compensation. These observation shows,
how many buses, which were out of constraint limit, managed to make it within the
constraint limit after compensation. A ratio of the difference of the number of these buses
(before and after compensation) to that of the total number of buses multiplied with
hundred gives percentage or Rate of under voltage mitigated nodes(RUVMN). Higher the
value of RUVMN for a particular node, more is the chances of placing a DSTATCOM on
that bus.
0 5 10 15 20 25 30 350.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Number of Buses
Bus V
oltage (
in p
.u)
28
Table 3.4 Tabulation for RUVMN of 33-Bus Radial Distribution System
Nodes No. RUVMN(in %)
1 0
2 6.0606
3 18.1818
4 24.2424
5 45.4545
6 63.6364
7 39.3939
8 36.3636
9 33.3333
10 30.3030
11 27.2727
12 24.2424
13 21.2121
14 18.1818
15 12.1212
16 9.0909
17 6.0606
18 3.0303
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 27.2727
27 24.2424
28 21.2121
29 18.1818
30 15.1515
31 12.1212
32 6.0606
33 3.0303
29
From the above tabulation we can observe that Bus No. 5,6,7,8 are having high value of
RUVMN. This makes all these Buses much desirable for DSTATCOM placement.
Figure 3.4 Graph comparing the Rate of under voltage mitigation for all 33-
Buses
CASE II: With fixed rating DSTATCOM.
In this case a specific rating of DSTATCOM is assumed. If the reactive power calculated
from Eq.2.16 is greater than the maximum reactive power rating of D-STATACOM, the
injected reactive power of DSTATCOM is set to its maximum rating and is considered as
a negative constant value in load model for the compensating node, and the load flow
program is solved in a normal way as if there is no DSTATCOM. In other case if
calculated rating is less than DSTATCOM rating, then the case switches to variable
rating DSTATCOM (CASE I).
0 5 10 15 20 25 30 350
10
20
30
40
50
60
70
No. Buses
RU
VM
N
30
Table 3.5 Comparison of Compensation Between Bus No. 3 , 6, 28 and 32 with a
fixed 2 MVAr rating DSTATCOM
Compensated Busesβ
Compensate
d bus no. 3
Compensate
d bus no. 6
Compensate
d bus no. 28
Compensate
d bus no. 32 Bus No. β
1 1.0000 1.0000 1.0000 1.0000
2 0.9976 0.9976 0.9976 0.9976
3 0.9867 0.9869 0.9868 0.9867
4 0.9792 0.9818 0.9818 0.9815
5 0.9718 0.9770 0.9770 0.9766
6 0.9534 0.9679 0.9679 0.9672
7 0.9499 0.9645 0.9644 0.9637
8 0.9363 0.9511 0.9511 0.9503
9 0.9300 0.9449 0.9449 0.9441
10 0.9242 0.9392 0.9391 0.9384
11 0.9233 0.9384 0.9383 0.9375
12 0.9218 0.9369 0.9368 0.9360
13 0.9156 0.9308 0.9307 0.9300
14 0.9134 0.9286 0.9285 0.9277
15 0.9119 0.9272 0.9271 0.9263
16 0.9106 0.9258 0.9257 0.9250
17 0.9085 0.9238 0.9237 0.9230
18 0.9079 0.9232 0.9231 0.9224
19 0.9971 0.9971 0.9971 0.9971
20 0.9935 0.9935 0.9935 0.9935
21 0.9928 0.9928 0.9928 0.9928
22 0.9922 0.9922 0.9922 0.9922
23 0.9831 0.9833 0.9833 0.9831
24 0.9765 0.9766 0.9766 0.9764
25 0.9732 0.9733 0.9733 0.9731
26 0.9515 0.9660 0.9673 0.9665
27 0.9489 0.9635 0.9667 0.9658
28 0.9375 0.9523 0.9676 0.9663
29 0.9294 0.9443 0.9593 0.9672
30 0.9258 0.9408 0.9559 0.9670
31 0.9217 0.9367 0.9519 0.9752
32 0.9208 0.9358 0.9510 0.9789
33 0.9205 0.9355 0.9507 0.9787
31
Table 3.6 RUVMN For a given 2 MVAr DSTATCOM In 33-Bus Distribution
System
Nodes No. RUVMN (in %)
1 0
2 3.0303
3 6.0606
4 12.1212
5 12.1212
6 18.1818
7 21.2121
8 39.3939
9 48.4848
10 48.4848
11 48.4848
12 48.4848
13 48.4848
14 45.4545
15 45.4545
16 45.4545
17 45.4545
18 45.4545
19 3.0303
20 3.0303
21 3.0303
22 3.0303
23 6.0606
24 6.0606
25 6.0606
26 18.1818
27 18.1818
28 33.3333
29 33.3333
30 33.3333
31 33.3333
32 33.3333
33 33.3333
32
Figure 3.5 Comparison of compensation at buses 3, 6, 28, 32 of 33-Bus Radial
Distribution System
By comparing the results obtained between table 3.4 and table 3.6 to that between
Table 3.3 and Table 3.5, we can observe that DSTATCOM has less effect when itβs
rating is specified. Also it becomes less desirable when the difference between the
required reactive power and maximum reactive rating of the DSTATCOM becomes
greater. It can also be observed that a DSTATCOM not only improves voltage profile of
downstream node , but also improves the voltage profile of uphill nodes.
3.2 DSTATCOM Placement on 69-Bus Radial Distribution
System
The 69-bus radial distribution system shown in Fig. 3.6 has the following characteristics:
No. of Buses: 69
No. of branches: 68
Slack Bus: 1
Base Voltage: 12.66 KV
Base MVA: 100 MVA
0 5 10 15 20 25 30 350.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Bus Number
Bus V
oltage(in p
.u)
33
Figure 3.6 69-Bus Radial distribution System.
The down stream nodes from the developed program are obtained and summarized in
Table 3.7.
34
Table 3.7 Down stream nodes for each node in 69-Bus Radial Distribution
System
Br
an
ch
N
o.
Sendi
ng
end
Bus
Receiving
end bus
Total
downstream
Buses
Bus Numbers
1 1 2 68
2,3,4,5,6,7,8,,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,2
4,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,,6
3,64,65,66,67,68,69
2 2 3 67
3,4,5,6,7,8,,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,4
4,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,,63,64,65,66,67,68,69
3 3 4 47
4,5,6,7,8,910,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,6
4,65,66,67,68,69
4 4 5 42
5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,2
6,27,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
69
5 5 6 41
6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
27,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,6
9
6 6 7 40 7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27
,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
7 7 8 39 8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,5
1,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
8 8 9 36 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,53,
54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
9 9 10 22 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,66,6
7,68,69
10 10 11 21 11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,66,67,68,69
11 11 12 18 12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,68,69
12 12 13 15 13,14,15,16,17,18,19,20,21,22,23,24,25,26,27
13 13 14 14 14,15,16,17,18,19,20,21,22,23,24,25,26,27
14 14 15 13 15,16,17,18,19,20,21,22,23,24,25,26,27
15 15 16 12 16,17,18,19,20,21,22,23,24,25,26,27
16 16 17 11 17,18,19,20,21,22,23,24,25,26,27
17 17 18 10 18,19,20,21,22,23,24,25,26,27
18 18 19 9 19,20,21,22,23,24,25,26,27
19 19 20 8 20,21,22,23,24,25,26,27
20 20 21 7 21,22,23,24,25,26,27
21 21 22 6 22,23,24,25,26,27
22 22 23 5 23,24,25,26,27
23 23 24 4 24,25,26,27
24 24 25 3 25,26,27
25 25 26 2 26,27
26 26 27 1 27
35
27 3 28 8 28,29,30,31,32,33,34,35
28 28 29 7 29,30,31,32,33,34,35
29 29 30 6 30,31,32,33,34,35
30 30 31 5 31,32,33,34,35
31 31 32 4 32,33,34,35
32 32 33 3 33,34,35
33 33 34 2 34,35
34 34 35 1 35
35 3 36 11 36,37,38,39,40,41,42,43,44,45,46
36 36 37 10 37,38,39,40,41,42,43,44,45,46
37 37 38 9 38,39,40,41,42,43,44,45,46
38 38 39 8 39,40,41,42,43,44,45,46
39 39 40 7 40,41,42,43,44,45,46
40 40 41 6 41,42,43,44,45,46
41 41 42 5 42,43,44,45,46
42 42 43 4 43,44,45,46
43 43 44 3 44,45,46
44 44 45 2 45,46
45 45 46 1 46
46 4 47 4 47,48,49,50
47 47 48 3 48,49,50
48 48 49 2 49,50
49 49 50 1 50
50 8 51 2 51,52
51 51 52 1 52
52 9 53 13 53,54,55,56,57,58,59,60,61,62,63,64,65
53 53 54 12 54,55,56,57,58,59,60,61,62,63,64,65
54 54 55 11 55,56,57,58,59,60,61,62,63,64,65
55 55 56 10 56,57,58,59,60,61,62,63,64,65
56 56 57 9 57,58,59,60,61,62,63,64,65
57 57 58 8 58,59,60,61,62,63,64,65
58 58 59 7 59,60,61,62,63,64,65
59 59 60 6 60,61,62,63,64,65
60 60 61 5 61,62,63,64,65
61 61 62 4 62,63,64,65
62 62 63 3 63,64,65
63 63 64 2 64,65
64 64 65 1 65
65 11 66 2 66,67
66 66 67 1 67
67 12 68 2 68,69
68 68 69 1 69
Load flow solution without compensation for 69 bus RDS obtained from the developed
program is summarized in Table 3.8.
36
Table 3.8 Base Distribution System Load flow for a 69-Bus Radial Network
Bus Number Bus Voltage (in p.u) Phase Angle(in deg.)
1 1.0000 0
2 1.0000 -0.0000
3 0.9999 -0.0000
4 0.9998 -0.0001
5 0.9990 -0.0003
6 0.9901 0.0009
7 0.9808 0.0021
8 0.9786 0.0024
9 0.9774 0.0026
10 0.9724 0.0040
11 0.9713 0.0044
12 0.9682 0.0053
13 0.9653 0.0061
14 0.9624 0.0069
15 0.9595 0.0077
16 0.9590 0.0078
17 0.9581 0.0081
18 0.9581 0.0081
19 0.9576 0.0082
20 0.9573 0.0083
21 0.9568 0.0085
22 0.9568 0.0085
23 0.9568 0.0085
24 0.9566 0.0086
25 0.9564 0.0086
26 0.9564 0.0087
27 0.9563 0.0087
28 0.9999 -0.0000
29 0.9999 -0.0001
30 0.9997 -0.0001
31 0.9997 -0.0000
32 0.9996 -0.0000
33 0.9993 0.0001
34 0.9990 0.0002
35 0.9989 0.0002
36 0.9999 -0.0001
37 0.9997 -0.0002
38 0.9996 -0.0002
39 0.9995 -0.0002
40 0.9995 -0.0002
41 0.9988 -0.0004
42 0.9986 -0.0005
43 0.9985 -0.0005
44 0.9985 -0.0005
45 0.9984 -0.0005
46 0.9984 -0.0005
37
47 0.9998 -0.0001
48 0.9985 -0.0009
49 0.9947 -0.0033
50 0.9942 -0.0037
51 0.9785 0.0024
52 0.9785 0.0024
53 0.9746 0.0029
54 0.9714 0.0034
55 0.9669 0.0040
56 0.9626 0.0046
57 0.9401 0.0115
58 0.9290 0.0151
59 0.9247 0.0165
60 0.9197 0.0183
61 0.9123 0.0195
62 0.9120 0.0196
63 0.9116 0.0196
64 0.9097 0.0199
65 0.9092 0.0200
66 0.9713 0.0044
67 0.9713 0.0044
68 0.9679 0.0054
69 0.9678 0.0054
The bus voltage profile resulted after the load flow solution is shown in Fig. 3.7.
Figure 3.7 Plot for Load Flow Results of 69-Bus Radial Distribution System
0 10 20 30 40 50 60 700.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Bus Number
Bus V
oltage(in p
.u)
38
Case I With fixed voltage DSTATCOM
The effect of compensation by fixed voltage DSTATCOM applied to buses 8, 57 and 59
one by one is summarized in Table. 3.8 and also shown in Fig. 3.8.
Table 3.9 Comparison of Compensation between Bus No. 8, 59 and 57 with fixed
voltage DSTATCOM
Bus No. Compensation on
Bus No.8
Compensation on
Bus No.59
Compensation on
Bus No.57
1 1.0000 1.0000 1.0000
2 1.0000 1.0000 1.0000
3 0.9999 0.9999 0.9999
4 0.9998 0.9998 0.9998
5 0.9990 0.9991 0.9991
6 0.9903 0.9906 0.9905
7 0.9812 0.9817 0.9816
8 1.0000 0.9796 0.9794
9 0.9989 0.9786 0.9784
10 0.9940 0.9736 0.9734
11 0.9929 0.9725 0.9723
12 0.9898 0.9693 0.9691
13 0.9870 0.9664 0.9662
14 0.9842 0.9635 0.9633
15 0.9814 0.9606 0.9604
16 0.9808 0.9601 0.9599
17 0.9800 0.9592 0.9590
18 0.9800 0.9592 0.9590
19 0.9795 0.9588 0.9586
20 0.9792 0.9585 0.9583
21 0.9788 0.9580 0.9578
22 0.9787 0.9580 0.9578
23 0.9787 0.9579 0.9577
24 0.9785 0.9577 0.9575
25 0.9784 0.9576 0.9574
26 0.9783 0.9575 0.9573
27 0.9783 0.9575 0.9573
28 0.9999 0.9999 0.9999
29 0.9999 0.9999 0.9999
30 0.9997 0.9997 0.9997
31 0.9997 0.9997 0.9997
32 0.9996 0.9996 0.9996
33 0.9993 0.9994 0.9994
34 0.9990 0.9990 0.9990
35 0.9989 0.9989 0.9989
36 0.9999 0.9999 0.9999
37 0.9997 0.9997 0.9997
39
38 0.9996 0.9996 0.9996
39 0.9995 0.9995 0.9995
40 0.9995 0.9995 0.9995
41 0.9988 0.9988 0.9988
42 0.9986 0.9986 0.9986
43 0.9985 0.9985 0.9985
44 0.9985 0.9985 0.9985
45 0.9984 0.9984 0.9984
46 0.9984 0.9984 0.9984
47 0.9998 0.9998 0.9998
48 0.9985 0.9986 0.9985
49 0.9947 0.9947 0.9947
50 0.9942 0.9942 0.9942
51 1.0000 0.9796 0.9794
52 1.0000 0.9796 0.9794
53 0.9962 0.9760 0.9757
54 0.9930 0.9730 0.9727
55 0.9886 0.9688 0.9685
56 0.9844 0.9648 0.9644
57 0.9625 0.9441 1.0000
58 0.9517 0.9339 0.9896
59 0.9475 1.0000 0.9856
60 0.9426 0.9954 0.9809
61 0.9354 0.9885 0.9740
62 0.9351 0.9883 0.9737
63 0.9347 0.9879 0.9734
64 0.9329 0.9862 0.9716
65 0.9323 0.9856 0.9711
66 0.9929 0.9724 0.9722
67 0.9929 0.9724 0.9722
68 0.9895 0.9690 0.9688
69 0.9895 0.9690 0.9688
Figure 3.8 Plot Comparing Improvement in Voltage Profile of Buses 8, 59, 57
0 10 20 30 40 50 60 700.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Bus Number
Bus V
oltage(in p
.u)
40
The RUVMN resulted due to fixed voltage DSTATCOM is summarized in Table 3.10.
and also presented in Fig. 3.9. The maximum value is obtained at when DSTATCOM is
placed at bus 57.
Table 3.10 RUVMN of variable DSTATCOM Rating for a 69-Bus Radial
Distribution System
Bus No. RUVMN (in %)
1 0
2 0
3 0
4 0
5 0
6 1.4493
7 1.4493
8 2.8986
9 2.8986
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
41
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
48 0
49 0
50 0
51 0
52 0
53 4.3478
54 4.3478
55 5.7971
56 10.1449
57 13.0435
58 11.5942
59 10.1449
60 8.6957
61 7.2464
62 5.7971
63 4.3478
64 2.8986
65 1.4493
66 0
67 0
68 0
69 0
Figure 3.9 RUVMN for 69-Bus Radial Distribution System.
0 10 20 30 40 50 60 700
2
4
6
8
10
12
14
Bus Number
RU
VM
N(in %
)
42
Case II Fixed rating DSTATCOM
The effect of compensation of 2 MVAR by DSTATCOM on randomly chosen bus
numbers 8, 27 and 69 is summarized in Table 3.11.
Table 3.11 Comparison between Bus voltage of Bus No.8,27,69 using fixed rating
DSTATCOM
Compensated Busesβ Compensation on
Bus no.8
Compensation on
bus No.27
Compensation On
Bus No.69 Bus NO. β
1 1.0000 1.0000 1.0000
2 1.0000 1.0000 1.0000
3 1.0000 1.0000 1.0000
4 0.9999 0.9999 0.9999
5 0.9995 0.9994 0.9995
6 0.9929 0.9925 0.9928
7 0.9862 0.9852 0.9859
8 0.9845 0.9835 0.9843
9 0.9834 0.9826 0.9835
10 0.9784 0.9802 0.9817
11 0.9774 0.9797 0.9814
12 0.9742 0.9789 0.9811
13 0.9713 0.9794 0.9782
14 0.9684 0.9801 0.9754
15 0.9656 0.9811 0.9726
16 0.9651 0.9813 0.9720
17 0.9642 0.9818 0.9712
18 0.9642 0.9818 0.9712
19 0.9637 0.9826 0.9707
20 0.9634 0.9831 0.9704
21 0.9629 0.9840 0.9699
22 0.9629 0.9840 0.9699
23 0.9629 0.9846 0.9699
24 0.9627 0.9858 0.9697
25 0.9625 0.9887 0.9695
26 0.9625 0.9899 0.9695
27 0.9625 0.9906 0.9694
28 1.0000 1.0000 1.0000
29 0.9999 0.9999 0.9999
30 0.9998 0.9998 0.9998
31 0.9997 0.9997 0.9997
32 0.9996 0.9996 0.9996
33 0.9994 0.9994 0.9994
43
34 0.9990 0.9990 0.9990
35 0.9990 0.9990 0.9990
36 0.9999 0.9999 0.9999
37 0.9998 0.9998 0.9998
38 0.9996 0.9996 0.9996
39 0.9996 0.9996 0.9996
40 0.9996 0.9996 0.9996
41 0.9989 0.9989 0.9989
42 0.9986 0.9986 0.9986
43 0.9985 0.9985 0.9985
44 0.9985 0.9985 0.9985
45 0.9984 0.9984 0.9984
46 0.9984 0.9984 0.9984
47 0.9999 0.9999 0.9999
48 0.9986 0.9986 0.9986
49 0.9948 0.9948 0.9948
50 0.9942 0.9942 0.9942
51 0.9845 0.9835 0.9842
52 0.9845 0.9834 0.9842
53 0.9806 0.9799 0.9807
54 0.9774 0.9766 0.9775
55 0.9730 0.9722 0.9730
56 0.9686 0.9678 0.9687
57 0.9463 0.9455 0.9464
58 0.9353 0.9345 0.9354
59 0.9311 0.9303 0.9311
60 0.9261 0.9253 0.9261
61 0.9188 0.9179 0.9188
62 0.9185 0.9176 0.9185
63 0.9181 0.9172 0.9181
64 0.9162 0.9153 0.9162
65 0.9156 0.9148 0.9157
66 0.9773 0.9796 0.9813
67 0.9773 0.9796 0.9813
68 0.9739 0.9785 0.9839
69 0.9739 0.9785 0.9839
3.3 Concluding Remarks
From the above study it is observed that the developed algorithm works well to
model DSTATCOM operation in Fixed voltage mode and Fixed rating VAR
compensation mode. The Fixed voltage mode operation of DSTATCOM is more suited
for improving the voltage profile of buses than the fixed rating modes.
44
CHAPTER 4 CONCLUSIONS AND SCOPE FOR
FURTHER WORK
4.1 CONCLUSIONS
The work has been carried out with an aim to identify the best suitable node for
DSTATCOM placement in a distribution network. Study has been carried out with both
fixed rating and variable rating DSTATCOM and a comparison has been made between
them. To perform this act initially load flow is performed with backward and forward
sweep method and then after modeling the DSTATCOM, again load flow is done with
DSTATCOM attachment on the desired bus. Study has been carried out on 33-Bus and
69-Bus radial distribution system taking into account that the system is completely in
steady state.
This compensation yield better voltage profile.
Method for identifying bus for DSTATCOM placement is easy and
effective.
The compensation by operating the DSTATCOM in fixed voltage mode is
effective for improving the voltage profile.
4.2 SCOPE FOR FUTURE WORK
Tough much work as compared to capacitor placement is not there for DSTATCOM
placement in Distribution system load flow , this leaves much scope for further work in
many related areas. Following are the areas identified for further studies
1. Modeling of DSTATCOM for load flow in dynamic loading condition.
2. Modeling of DSTATCOM for three-phase unbalanced load.
3. Modeling of DSTATCOM for other topologies such as mesh distribution
network.
45
REFERENCES:
1. S. Ghosh and D. Das, βMethod for load-flow solution of radial distribution
Networksβ, IEE Proceedings on Generation, Transmission & Distribution, Vol.
146, No. 6, pp. 641-648, 1999.
2. R. Ranjan and D. Das, βSimple and efficient computer algorithm to solve radial
distribution networksβ, Electric Power Components and Systems, Vol. 31, No. 1,
pp. 95-107, 2003.
3. M. M. A. Salama, J. Liu and R. R. Mansour, βAn efficient power flow algorithm
for distribution systems with polynomial loadβ, International Journal of
Electrical Engineering Education, Vol. 39, No. 4, pp. 372-386, 2002.
4. R. Berg, E.S. Hawkins and W.W. Pleines, βMechanized Calculation of
Unbalanced Load Flow on Radial Distribution Circuitsβ, IEEE Transactions on
Power Apparatus and Systems, Vol.4, pp. 415 β 421, 1967.
5. M. E. Baran and F. F. Wu, βOptimal Sizing of Capacitor Placed on Radial
Distribution Systems,β IEEE Transaction on Power Delivery, Vol.2, pp.735β
743, January 1989.
6. E. Perez, V. Simha and B. Gou, βInitial Results in An Approximate Optimal
Capacitor Placement for Radial Distribution Systemsβ, IEEE Power
Engineering Society General Meeting, Vol. 1, pp. 336 β 341, Denver, Colorado,
6-10 June, 2004.
7. J. Balakumaran and K. Thanuskodi, βLoss Reduction In Radial Distribution
Systems By Capacitor Placement: Fuzzy Techniqueβ, IEEE Conference on
Etech pp. 23 β 29, Karachi, Pakistan, 31 July, 2004.
46
8. K. H. Kim and S. K. You, βVoltage Profile Improvement by Capacitor
Placement and Control in Unbalanced Distribution Systems using GAβ, IEEE
Power Engineering Society Summer Meeting, vol. 2, pp. 800 β
805,Edmonton,Alberta,Canada,18-22 July, 1999.
9. H. Mori and Y. Ogita,βCapacitor placement using parallel tabu search in
distribution systemsβ, IEEE International Conference Proceedings on Systems,
Man, and Cybernetics, vol.6, pp. 521 - 526 1999.
10. B. Singh and J. Solanki, βA comparison of control algorithms for
DSTATCOMβ, IEEE Transactions on Industrial Electronics, Vol. 56, No. 7, pp.
2738-2745,2009.
11. M. H. Haque, βCompensation of distribution system voltage sag by DVR and D-
STATCOMβ, IEEE Porto Power Tech Proceedings,vol.1,Porto, Portugal, 10-13
Sept,2001.
12. P.S. Sensarma, K.R. Padiyar and V. Ramanarayanan., βAnalysis and
performance evaluation of a Distribution STATCOM for compensating voltage
fluctuationsβ, IEEE Transactions on Power Delivery, Vol. 16, pp.259-264,
2001.
13. S.M. Ramsay, P.E. Cronin, R.J. Nelson, J. Bian and F.E. Menendez, βUsing
Distribution Static Compensators (DSTATCOMs) to Extend the Capability of
Voltage-limited Distribution Feedersβ, The 39th Annual Conf. on Rural Electric
Power, pp.18-24, Fort Worth,Texas,28-30 April,1996.
14. H. Akagi , E. H. Watanabe and M. Aredes, βInstantaneous power theory and
application to power conditioningβ, Hoboken, NJ. Wiley, 2007.
15. B. S. Chen and Y. Y. Hsu, βA minimal harmonic controller for a STATCOMβ,
IEEE Transactions on Industrial Electronics, Vol. 55, No. 2, pp. 655-664, 2008.
16. M. Hosseini, S. H. Ali and F. H. Mahmud, βModeling of D-STATCOM in
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No. 10, pp. 1532-1542, 2007.
47
APPENDIX A
Table (A.1) Line data of 33- Bus Radial Distribution system
Branch No. Sending-end
bus
Receiving-end
bus
Branch
Resistance(Ξ©)
Branch
reactance(Ξ©)
1 1 2 0.0922 0.0477
2 2 3 0.4930 0.2511
3 3 4 0.3660 0.1864
4 4 5 0.3811 0.1941
5 5 6 0.8190 0.7070
6 6 7 0.1872 0.6188
7 7 8 1.7114 1.2351
8 8 9 1.0300 0.7400
9 9 10 1.0040 0.7400
10 10 11 0.1966 0.0650
11 11 12 0.3744 0.1238
12 12 13 1.4680 1.1550
13 13 14 0.5416 0.7129
14 14 15 0.5910 0.5260
15 15 16 0.7463 0.5450
16 16 17 1.2890 1.7210
17 17 18 0.7320 0.5740
18 2 19 0.1640 0.1565
19 19 20 1.5042 1.3554
20 20 21 0.4095 0.4784
21 21 22 0.7089 0.9373
22 3 23 0.4512 0.3083
23 23 24 0.8980 0.7091
24 24 25 0.8960 0.7011
25 6 26 0.2030 0.1034
26 26 27 0.2842 0.1447
27 27 28 1.0590 0.9337
28 28 29 0.8042 0.7006
29 29 30 0.5075 0.2585
30 30 31 0.9744 0.9630
31 31 32 0.3105 0.3619
32 32 33 0.3410 0.5302
48
Table (A.2) Load Data of 33-Bus Radial distribution System
Bus Number P(KW) Q(KVAR)
1 0 0
2 100 60
3 90 40
4 120 80
5 60 30
6 60 20
7 200 100
8 200 100
9 60 20
10 60 20
11 45 30
12 60 35
13 60 35
14 120 80
15 60 10
16 60 20
17 60 20
18 90 40
19 90 40
20 90 40
21 90 40
22 90 40
23 420 50
24 420 200
25 60 200
26 60 25
27 60 25
28 120 20
29 200 70
30 150 600
31 210 70
32 60 100
33 60 40
49
APPENDIX-B
Table (B.1) Line Data of 69-Bus Radial Distribution system
Branch No. Sending-end
Bus
Receiving-
end bus
Branch
Resistance(Ξ©)
Branch
reactance(Ξ©)
1 1 2 0.0005 0.0012
2 2 3 0.0005 0.0012
3 3 4 0.0015 0.0036
4 4 5 0.0215 0.0294
5 5 6 0.366 0.1864
6 6 7 0.381 0.1941
7 7 8 0.0922 0.047
8 8 9 0.0493 0.0251
9 9 10 0.819 0.2707
10 10 11 0.1872 0.0619
11 11 12 0.7114 0.2351
12 12 13 1.03 0.34
13 13 14 1.044 0.34
14 14 15 1.058 0.3496
15 15 16 0.1966 0.065
16 16 17 0.3744 0.1238
17 17 18 0.0047 0.0016
18 18 19 0.3276 0.1083
19 19 20 0.2106 0.069
20 20 21 0.3416 0.1129
21 21 22 0.014 0.0046
22 22 23 0.1591 0.0526
23 23 24 0.3463 0.1145
24 24 25 0.7488 0.2475
25 25 26 0.3089 0.1021
26 26 27 0.1732 0.0572
27 3 28 0.0044 0.0108
28 28 29 0.064 0.1565
29 29 30 0.3978 0.1315
30 30 31 0.0702 0.0232
31 31 32 0.351 0.116
32 32 33 0.839 0.2816
33 33 34 1.708 0.5646
34 34 35 1.474 0.4873
35 3 36 0.0044 0.0108
36 36 37 0.064 0.1565
37 37 38 0.1053 0.123
38 38 39 0.0304 0.0355
39 39 40 0.0018 0.0021
40 40 41 0.7283 0.8509
41 41 42 0.31 0.3623
42 42 43 0.041 0.0478
50
43 43 44 0.0092 0.0116
44 44 45 0.1089 0.1373
45 45 46 0.0009 0.0012
46 4 47 0.0034 0.0084
47 47 48 0.0851 0.2083
48 48 49 0.2898 0.7091
49 49 50 0.0822 0.2011
50 8 51 0.0928 0.0473
51 51 52 0.3319 0.114
52 9 53 0.174 0.0886
53 53 54 0.203 0.1034
54 54 55 0.2842 0.1447
55 55 56 0.2813 0.1433
56 56 57 1.59 0.5337
57 57 58 0.7837 0.263
58 58 59 0.3042 0.1006
59 59 60 0.3861 0.1172
60 60 61 0.5075 0.2585
61 61 62 0.0974 0.0496
62 62 63 0.145 0.0738
63 63 64 0.7105 0.3619
64 64 65 1.041 0.5302
65 65 66 0.2012 0.0611
66 66 67 0.0047 0.0014
67 67 68 0.7394 0.2444
68 68 69 0.0047 0.0016
51
Table (B.2) Bus Data of 69-bus Radial distribution system
Bus Number P(KW) Q(KVAR)
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
6 2.6 2.2
7 40.4 30
8 75 54
9 30 22
10 28 19
11 145 104
12 145 104
13 8 5
14 8 5
15 0 0
16 45 30
17 60 35
18 60 35
19 0 0
20 1 0.6
21 114 81
22 5 3.5
23 0 0
24 28 20
25 0 0
26 14 10
27 14 10
28 26 18.6
29 26 18.6
30 0 0
31 0 0
32 0 0
33 10 10
34 14 14
35 4 4
36 26 18.55
37 26 18.55
38 0 0
39 24 17
40 24 17
41 102 1
42 0 0
43 6 4.3
44 0 0
45 39.22 26.3
52
46 39.22 26.3
47 0 0
48 79 56.4
49 384.7 274.5
50 384.7 274.5
51 40.5 28.3
52 3.6 2.7
53 4.35 3.5
54 26.4 19
55 24 17.2
56 0 0
57 0 0
58 0 0
59 100 72
60 0 0
61 1244 888
62 32 23
63 0 0
64 227 162
65 59 42
66 18 13
67 18 13
68 28 20
69 28 20